The erythrocyte membrane is modelled as a two dimensional viscoelastic continuum that evolves under the application of stress. The present analysis on the erythrocyte membrane is motivated by the recent development of knowledge on its molecular structure and by its complex behavior exhibited in dynamic micropipette testing and in tank treading during shear flow. The proposed constitutive equations have the form similar to that of a two dimensional Kelvin model with a constant area condition. However, the membrane viscosity is made to depend on the rate of strain and the elastic strain tensor is measured from the evolving preferred configuration. The evolution of the preferred configuration is given by a rate equation. The material constants appearing in the proposed constitutive equations may be useful indicators of the biochemical state of the membrane in health and disease.